This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
import Data.List (elemIndex); import Data.Maybe (fromJust) a262429 = (+ 1) . fromJust . (`elemIndex` a262411_list)
a262435 n = a262435_list !! (n-1) a262435_list = [x | x <- [1..], a262411 x == x]
See A262411.
import Data.List (inits, tails, intersect, delete)
a262412 n = a262412_list !! (n - 1)
a262412_list = 1 : f [1] (drop 2 a030341_tabf) where
f xs tss = g tss where
g (ys:yss) | null (intersect its $ tail $ inits ys) &&
null (intersect tis $ init $ tails ys) = g yss
| otherwise = (foldr (\t v -> 10 * v + t) 0 ys) :
f ys (delete ys tss)
its = init $ tails xs; tis = tail $ inits xs
-- Reinhard Zumkeller, Sep 22 2015
The first terms of the sequence are: +----+---------+ | n | a(n) | +----+---------+ | 1 | 1 | | 2 | 10 | | 3 | 11 | | 4 | 12 | | 5 | 2 | | 6 | 20 | | 7 | 22 | | 8 | 21 | | 9 | 13 | | 10 | 3 | | 11 | 23 | | 12 | 30 | | 13 | 33 | | 14 | 31 | | 15 | 14 | | 16 | 4 | | 17 | 24 | | 18 | 32 | | 19 | 25 | | 20 | 5 | +----+---------+
import Data.List (inits, tails, intersect, delete)
a262323 n = a262323_list !! (n-1)
a262323_list = 1 : f "1" (map show [2..]) where
f xs zss = g zss where
g (ys:yss) | null (intersect its $ tail $ inits ys) &&
null (intersect tis $ init $ tails ys) = g yss
| otherwise = (read ys :: Int) : f ys (delete ys zss)
its = init $ tails xs; tis = tail $ inits xs
-- Reinhard Zumkeller, Sep 21 2015
See Links section.
def overlaps(a, b):
s, t = sorted([str(a), str(b)], key = lambda x: len(x))
if any(t.startswith(s[i:]) for i in range(len(s))): return True
return any(t.endswith(s[:i]) for i in range(1, len(s)+1))
def aupto(nn):
alst, aset = [1], {1}
for n in range(2, nn+1):
an = 1
while True:
while an in aset: an += 1
if overlaps(an, alst[-1]): alst.append(an); aset.add(an); break
an += 1
return alst
print(aupto(67)) # Michael S. Branicky, Jan 10 2021
Table of initial terms: the HEX column gives the hexadecimal representation with aligned overlapping digits. . n | a(n) | HEX n | a(n) | HEX n | a(n) | HEX . ----+------+------- ----+------+------- ----+------+------- . 1 | 1 | 1 25 | 38 | 26 49 | 44 | 2C . 2 | 16 | 10 26 | 66 | 42 50 | 114 | 72 . 3 | 17 | 11 27 | 39 | 27 51 | 45 | 2D . 4 | 18 | 12 28 | 7 | 7 52 | 13 | D . 5 | 2 | 2 29 | 23 | 17 53 | 29 | 1D . 6 | 32 | 20 30 | 81 | 51 54 | 129 | 81 . 7 | 34 | 22 31 | 24 | 18 55 | 30 | 1E . 8 | 33 | 21 32 | 8 | 8 56 | 14 | E . 9 | 19 | 13 33 | 40 | 28 57 | 46 | 2E . 10 | 3 | 3 34 | 82 | 52 58 | 130 | 82 . 11 | 35 | 23 35 | 41 | 29 59 | 47 | 2F . 12 | 48 | 30 36 | 9 | 9 60 | 15 | F . 13 | 51 | 33 37 | 25 | 19 61 | 31 | 1F . 14 | 49 | 31 38 | 97 | 61 62 | 145 | 91 . 15 | 20 | 14 39 | 26 | 1A 63 | 57 | 39 . 16 | 4 | 4 40 | 10 | A 64 | 67 | 43 . 17 | 36 | 24 41 | 42 | 2A 65 | 52 | 34 . 18 | 50 | 32 42 | 98 | 62 66 | 64 | 40 . 19 | 37 | 25 43 | 43 | 2B 67 | 68 | 44 . 20 | 5 | 5 44 | 11 | B 68 | 69 | 45 . 21 | 21 | 15 45 | 27 | 1B 69 | 80 | 50 . 22 | 65 | 41 46 | 113 | 71 70 | 53 | 35 . 23 | 22 | 16 47 | 28 | 1C 71 | 83 | 53 . 24 | 6 | 6 48 | 12 | C 72 | 54 | 36
import Data.List (inits, tails, intersect, delete, genericIndex)
a262460 n = genericIndex a262460_list (n - 1)
a262460_list = 1 : f [1] (drop 2 a262437_tabf) where
f xs tss = g tss where
g (ys:yss) | null (intersect its $ tail $ inits ys) &&
null (intersect tis $ init $ tails ys) = g yss
| otherwise = (foldr (\t v -> 16 * v + t) 0 ys) :
f ys (delete ys tss)
its = init $ tails xs; tis = tail $ inits xs
import Data.List (elemIndex); import Data.Maybe (fromJust) a262461 = (+ 1) . fromJust . (`elemIndex` a262460_list)
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